Brownian Motion

[J_B_]

Is there a particular path that is impossible for a particle under Brownian Motion? For example, if a particle is placed in the center of a square of liquid, is it A) impossible that it would move in a straight line to the edge, or is it B) just highly unlikely?

I would think the answer is B, but to be honest, I'm not completely sure.

 

[HARK!]

It would seem to me that if the particle started in the center of a cube, that it would be more likely that the particle would travel in a straight line, perpendicular to a face of that cube, than in a straight line to a vertex of that cube; as a vertex would be at a greater distance from the center, than a face.

With random motion, from one given point to the next, it would be possible for the particle to take any path, to any point within the cube.

 

[Hans Blaster]

Is there a particular path that is impossible for a particle under Brownian Motion? For example, if a particle is placed in the center of a square of liquid, is it A) impossible that it would move in a straight line to the edge, or is it B) just highly unlikely?

I would think the answer is B, but to be honest, I'm not completely sure.

Brownian motion is the motion of microscopic particles buffeted about by molecules. If it wasn't bouncing about in random directions it wouldn't really be Brownian motion.

 

[J_B_]

It would seem to me that if the particle started in the center of a cube, that it would be more likely that the particle would travel in a straight line, perpendicular to a face of that cube, than in a straight line to a vertex of that cube; as a vertex would be at a greater distance from the center, than a face.

With random motion, from one given point to the next, it would be possible for the particle to take any path, to any point within the cube.

If I interpret you correctly, you're saying B is the correct choice. I would think so - just looking for confirmation.

 

[J_B_]

Brownian motion is the motion of microscopic particles buffeted about by molecules. If it wasn't bouncing about in random directions it wouldn't really be Brownian motion.

I understand. So the particle starts in the center. We roll the dice. It moves in some random direction and moves closer to an edge. We roll the dice again. It's an independent event, so all directions are possible, which means it's possible it takes another step in the same direction. And so on.

It seems then, though it's unlikely, that one possible random path is a straight line to the edge.

 

[HARK!]

If I interpret you correctly, you saying B is the correct choice. I would think so - just looking for confirmation.

Yes.

Look at it this way. A particle is set in motion, with direction, on impact. That motion is slowed with friction until its' next impact. That impact can move it in any direction, including the direction in which it was already, or had previously, moved in. The process repeats itself. The chances of it moving in a straight line are the same as it moving in any other path.

An easier way to envision this might be to compare dice rolls. The chances of rolling three 1s in a row, are the same as rolling three 5s in a row, are the same as rolling 1 then 2 then 3, or 2, then 5, then 2 again.

The three 1s in a row, and the three 5s in a row, are straights.

 

[Mark Quayle]

Brownian motion is the motion of microscopic particles buffeted about by molecules. If it wasn't bouncing about in random directions it wouldn't really be Brownian motion.

Agreed. In fact, the question here is, how do you decide what to call a straight line. If it is geometrically (absolutely) straight, it would lose no mass, gain no mass, and be unaffected by any force but whatever impelled it or draws it. That sounds impossible for a liquid suspension.

 

[Mark Quayle]

Yes.

Look at it this way. A particle is set in motion, with direction, on impact. That motion is slowed with friction until its' next impact. That impact can move it in any direction, including the direction in which it was already, or had previously, moved in. The process repeats itself. The chances of it moving in a straight line are the same as it moving in any other path.

An easier way to envision this might be to compare dice rolls. The chances of rolling three 1s in a row, are the same as rolling three 5s in a row, are the same as rolling 1 then 2 then 3, or 2, then 5, then 2 again.

The three 1s in a row, and the three 5s in a row, are straights.

But friction itself IS impact. A lot of them, actually.

 

[Mark Quayle]

I understand. So the particle starts in the center. We roll the dice. It moves in some random direction and moves closer to an edge. We roll the dice again. It's an independent event, so all directions are possible, which means it's possible it takes another step in the same direction. And so on.

It seems then, though it's unlikely, that one possible random path is a straight line to the edge.

What made it move? Will that continue to be its only cause of motion?

 

[HARK!]

But friction itself IS impact. A lot of them, actually.

Good point.

 

[Bradskii]

Is there a particular path that is impossible for a particle under Brownian Motion? For example, if a particle is placed in the center of a square of liquid, is it A) impossible that it would move in a straight line to the edge, or is it B) just highly unlikely?

I would think the answer is B, but to be honest, I'm not completely sure.

All directions are equally likely. But if you select directions, they are each impossibly unlikely. If 4 aces represents a straight line and 2, 5, J and K each of a different suit represents a wobbly line, then drawing those 4 cards are both as likely as each other.

 

[J_B_]

Agreed. In fact, the question here is, how do you decide what to call a straight line. If it is geometrically (absolutely) straight, it would lose no mass, gain no mass, and be unaffected by any force but whatever impelled it or draws it. That sounds impossible for a liquid suspension.

I don't understand what you're saying here, but it sounds like you're advocating for choice A. If so, you'll need to elaborate more.

 

[J_B_]

All directions are equally likely. But if you select directions, they are each impossibly unlikely. If 4 aces represents a straight line and 2, 5, J and K each of a different suit represents a wobbly line, then drawing those 4 cards are both as likely as each other.

OK. So is it A, B, ... or are you describing a 3rd option C?

 

[Mark Quayle]

I don't understand what you're saying here, but it sounds like you're advocating for choice A. If so, you'll need to elaborate more.

It's B, but nearly A. At least, according to Google's version of Brownian motion, where the "particle" is suspended in a liquid. (I'm not too keen on the loose use of the word 'particle' (pretty obviously not meaning sub-atomic particle) there, but anyway.)

 

[J_B_]

It's B, but nearly A. At least, according to Google's version of Brownian motion, where the "particle" is suspended in a liquid. (I'm not too keen on the loose use of the word 'particle' (pretty obviously not meaning sub-atomic particle) there, but anyway.)

The use of the term particle is always context sensitive.

I'll go you one step further. I'll bet if you saw a particle moving in a straight line through the fluid you would suspect something other than Brownian motion.

 

[HARK!]

It's B, but nearly A. At least, according to Google's version of Brownian motion, where the "particle" is suspended in a liquid. (I'm not too keen on the loose use of the word 'particle' (pretty obviously not meaning sub-atomic particle) there, but anyway.)

Would a NaCl molecule, in solution, be considered a particle, or a liquid?

 

[essentialsaltes]

I think a liquid is too dense to even consider B an outside possibility. A particle will have surface interactions with the liquid molecules that would prevent straightline motion.

If the 'particle' were itself an atom, and the fluid were a gas, then we might be in B territory.

 

[essentialsaltes]

Would a NaCl molecule, in solution, be considered a particle, or a liquid?

In solution, they dissolve and you would have two particles: a positive sodium ion and a negative chloride ion.

 

[HARK!]

I'll bet if you saw a particle moving in a straight line through the fluid you would suspect something other than Brownian motion.

I might suspect that static electricity was driving it; but this is exactly why I try to abstain from treating assumptions as facts, when trying to solve problems.

It very well could be Brownian motion driving it.

 

[HARK!]

In solution, they dissolve and you would have two particles: a positive sodium ion and a negative chloride ion.

Nope. H2O will not break the molecular bond with the Na and Cl. It could be done with electrolysis through a semipermeable membrane ; but then that would consume water, leaving us with lye and bleach.